Your husband needs to grow up. This is worth fighting over. Not only did you not overreact–I would say your behavior was subdued. Perhaps there is more of a cultural allowance in your country for his behavior, but in straight psychological terms with regard to relationship and family, his behavior is at best immature and at worst irresponsible.
I would highly recommend couples therapy sooner rather than later. This sort of thing rarely gets better on its own. Second, I would make sure that you have at least one night where you go out and he has responsibility for your infant. This is important. Even if you just go to the library the idea is that you need to have some time for whatever you want to do, and he needs to learn how to become a parent. Finally, I would plan for time for the two of you to be together and for the three of you to be a family. Time alone for couples is essential and time shared as a family is precious.